Funding affordable housing and other social programs will require more tax dollars. But that does not mean that your taxes have to go up.
New construction grows the tax base, and improves efficiency. It's like buying in bulk!
For example, serving on the Zero Waste Commission, one of the things I did was review costs and rates for the City's garbage collection services, and compare it to other cities. One of the findings was that the cost to service a duplex is basically the same as that to service a single unit house, since the labor is the main cost, and the amount of labor needed is based on the number of times staff needs to stop and wheel a cart up to the truck.
True, some things such as streets and parks will require more maintenance with more people using them. Others, however, such as public art or storm sewers, cost the same regardless of how many people live on each block.
Finally, a lot of Berkeley's biggest costs - for example, earthquake retrofitting historic public buildings such as Old City Hall - are fixed costs. Having more homes and businesses to spread the cost over will reduce each individual's burden.